It sounds to me like when your Phantom tipped over the props were obstructed and I am guessing they were making a very loud noise. You were probably getting some sort of warning that the motors were obstructed. That would very quickly overheat the motors and could also fairly quickly melt the plastic. With the motor out of alignment you would not want to fly it. It would not respond correctly if it is out of alignment. It doesn't sound like a factory defect to me. I would suggest that when you get it repaired you learn how to recover it by hand. I find it a much safer way to recover my P3.

A picture or two would be a benefit of the doubt...
I need to see it to know, & a view from inside the shell would be even more telling...
Though, We all know how thin these shells can be, at the screw pocket locations too. Hehe

Everything the o p mentioned happened to me with the same results, except I hit a small branch that dropped my p3p and it landed tilting forward. It made the loud squealing sound, overheated, wouldn't respond to the CSC and I had to pull the battery to kill it. In my case the plastic melted enough that the rotor would light tap the top of the case when spinning.

As hot as the batteries get especially after a full run, they should always be pulled out immediately upon landing... The shell acts as an insulator. Pull the battery and let both sit for a minute or 2 depending on the shells temp and after it has cooled, put in the next battery and take off